{"id":7135,"date":"2011-11-08T14:32:14","date_gmt":"2011-11-08T14:32:14","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7135"},"modified":"2022-01-25T19:26:18","modified_gmt":"2022-01-25T19:26:18","slug":"um-fabricante","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7135","title":{"rendered":"Um fabricante"},"content":{"rendered":"<p><ul id='GTTabs_ul_7135' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7135' class='GTTabs_curr'><a  id=\"7135_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7135' ><a  id=\"7135_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_7135'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Um fabricante analisou os registos di\u00e1rios do n\u00famero de artigos vendidos por um dos seus representantes e elaborou a seguinte distribui\u00e7\u00e3o de probabilidades:<\/p>\n<table class=\" aligncenter\" style=\"width: 60%;\" border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">${{x}_{i}}$ &#8211; N.\u00ba de artigos vendidos<\/td>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">0<\/td>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">1<\/td>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">2<\/td>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">3<\/td>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">4<\/td>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">5<\/td>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">6<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">$P(X={{x}_{i}})$<\/td>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">0,1<\/td>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">0,35<\/td>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">0,3<\/td>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">0,1<\/td>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">$p$<\/td>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">0,07<\/td>\n<td style=\"text-align: center; border: #d2691e 1px solid;\">0,06<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol>\n<li>Calcule o valor de $p$.<\/li>\n<li>Sendo $\\mu $ o valor m\u00e9dio e $\\sigma $ o desvio padr\u00e3o da distribui\u00e7\u00e3o, qual \u00e9 a probabilidade do n\u00famero de vendas pertencer ao intervalo \\[\\left] \\mu -\\sigma ,\\mu +\\sigma\u00a0 \\right[\\].<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7135' onClick='GTTabs_show(1,7135)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7135'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Sabendo que $\\sum\\limits_{i=0}^{6}{{{p}_{i}}=1}$, vem: $0,1+0,35+0,3+0,1+p+0,07+0,06=1\\Leftrightarrow p=0,02$.<br \/>\n\u00ad<\/li>\n<li>O valor m\u00e9dio e o desvio padr\u00e3o da distribui\u00e7\u00e3o s\u00e3o, respetivamente:<br \/>\n\\[\\mu =0,1\\times 0+0,35\\times 1+0,3\\times 2+0,1\\times 3+0,02\\times 4+0,07\\times 5+0,06\\times 6=2,04\\]<br \/>\n\\[\\sigma =\\sqrt{0,1\\times {{(0-2,04)}^{2}}+0,35\\times {{(1-2,04)}^{2}}+&#8230;+0,07\\times {{(5-2,04)}^{2}}+0,06\\times {{(6-2,04)}^{2}}}=\\sqrt{2,5184}\\approx 1,59\\]<br \/>\nPortanto, a probabilidade do n\u00famero de vendas pertencer ao intervalo \\[]0,45;3,63[\\] \u00e9, aproximadamente, $p\\approx P(X=1)+P(X=2)+P(X=3)=0,35+0,3+0,1=0,75$.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7135' onClick='GTTabs_show(0,7135)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um fabricante analisou os registos di\u00e1rios do n\u00famero de artigos vendidos por um dos seus representantes e elaborou a seguinte distribui\u00e7\u00e3o de probabilidades: ${{x}_{i}}$ &#8211; N.\u00ba de artigos vendidos 0 1&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21024,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,245,244],"series":[],"class_list":["post-7135","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-probabilidades-e-combinatoria","tag-12-o-ano","tag-distribuicao-de-probabilidades","tag-variavel-aleatoria"],"views":3010,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/12V1Pag172-32_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7135","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7135"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7135\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21024"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7135"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7135"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}